Final answer:
To find the vertex of the graph of a quadratic function, use the vertex formula -b/2a where a and b are the coefficients of the quadratic function. The vertex coordinates are (-2.92, -9). None of the given options are correct.
Step-by-step explanation:
To find the vertex of the graph of a quadratic function, you can complete the square or use the vertex formula.
The vertex formula states that the x-coordinate of the vertex is given by -b/2a, where a and b are the coefficients of the quadratic function.
In this case, the quadratic function is ax²+bx+c = 0, where a = 4.90, b = 14.3, and c = -20.0.
Substituting the values into the formula, we get x = -14.3 / (2 * 4.90) = -2.92.
To find the corresponding y-coordinate, substitute x = -2.92 into the quadratic function.
Plugging the values into the function, we get y = 4.9 * (-2.92)² + 14.3 * (-2.92) - 20.0 = -9.
Therefore, the vertex of the graph is (-2.92, -9). The answer is not in the options provided, so none of the options A, B, C, or D are correct.